The Trump Administration asked the Supreme Court to stay "universal" injunctions issued by three separate district courts in cases challenging President Trump's EO purporting to deny birthright citizenship to certain individuals born within the United States.
The application does not ask the Court to weigh in on the underlying merits. But it nevertheless rehearses the Administration's arguments against birthright citizenship for individuals that the Administration says are not "subject to the jurisdiction thereof." (Short version: "The original public meaning of the term 'jurisdiction' refers [to] 'political jurisdiction' (which turns on whether a person owes allegiance to, and is entitled to protection from, the United States), not regulatory jurisdiction (which turns on whether a person must follow U.S. law).")
If the Court grants the Administration's request, the court rulings would still enjoin the Administration from denying birthright citizenship to parties before those courts. If the Court denies the request, the rulings stay in place, and the Administration could not enforce the EO nationwide pending further litigation.
Here's the Administration's arguments why universal, or nationwide, injunctions are unlawful:
Universal injunctions transgress constitutional limits on courts' powers, which extend only to "render[ing] a judgment or decree upon the rights of the litigants." Universal injunctions are also incompatible with "'foundational' limits on equitable jurisdiction." "[N]ationwide injunctions have not been good for the rule of law," and "ris[k] the perception of the federal courts as an apolitical branch." And universal injunctions compromise the Executive Branch's ability to carry out its functions, as administrations of both parties have explained.